Bob,
I'd suggest you do some more reading on the purpose behind bonding and bridging. It *sounds* like what you functionally need is to have a server with a single route upstream, not acting as a gateway, but where you want to be able to take a failure on one of the upstream network connections without losing connectivity.
If that is true, then look at bonding.
Bridging is typically used if you want to have a machine, perhaps acting as a transparent firewall join two physical network segments as if they are one logical network. It has nothing to do with network redundancy.
Note that bonding will only solve the redundancy problem if your upstream switches are redundant and all the upstream connections from there are redundant as well. (Bonding can have other purposes as well, such as increasing throughput, but I don't think that's relevent here.)
As an aside (and in case you run into it in your reading), multihoming is another way to receive redundancy, but unless you are an expert (or at least very experienced) in networking including DNS, routing, and exterior gateway protocols, as well as having your own ASN and directly assigned network blocks, then Don't Go There. And this type of multihoming is typically used only on border gateways. (Also, if you do multihoming wrong and start flapping then your peer networks will typically blacklist you and you lose *all* connectivity.)
Devin